2. A firm produces two products A and B. Both products need to undergo a pressmachine and a paining process. Every unit of product A needs 40 hours of thepress machine and 50 hours of the painting process. Similarly, every unit ofproduct B needs 40 hours of the press machine and 25 hours of the paintingprocess. Each unit of product A brings 600,000 yen of profit and every unit ofproduct B 400,000 yen. Every month, the total available time for the pressmachine is 480 hours and for the painting process 400 hours. Formulate thisproblem as a LP model and solve the model.

The linear function that needs to be optimized(maximize or minimize) is called the objective…

Answered: 2. A firm produces two products A and…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...

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If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.
Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
Glueco produces three types of glue on two differentproduction lines. Each line can be utilized by up to sevenworkers at a time. Workers are paid $500 per week onproduction line 1, and $900 per week on production line 2.A week of production costs $1,000 to set up production line1 and $2,000 to set up production line 2. During a week ona production line, each worker produces the number of unitsof glue shown in Table 12. Each week, at least 120 units ofglue 1, at least 150 units of glue 2, and at least 200 units ofglue 3 must be produced. Formulate an IP to minimize thetotal cost of meeting weekly demands.
A company manufactures two products A and B, and each of these products must be processed on two different machines. Product A requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product B requires 3 minute of work time per unit on machine 1 and 2 minutes of work time on machine 2. Each day 100 minutes are available on machine 1 and 200 minutes are available on machine 2. The profit of each unit of product A is $50 and the profit of each unit of product B is $60. (Let x = number of units of product A and y = number of units of product B). 1. Identify the variables. 2. Set up the objective function. 3. Give the constraints in mathematical expression. 4. Graph the constraints and identify the solution. 5. How many units of each product should be produced daily in order to maximize the company's profit? 6. What is that maximum profit daily?
2. A small company manufactures 3 different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 1 hr of fabrication and 2 hours of assembly, and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 1000 labor-hours of fabrication time and 800 labor-hours of assembly time available per week. The profit on each component A, B, and C is $7, 9, and 10 respectively. How many components of each type should the company manufacture each week in order to maximize its profit? What is the maximum profit?
For a particular process, originally each 200 units of product manufactured yielded 180 conforming units, 9 units that must be scrapped, and the remaining units that must be reprocessed. Each scrapped unit results in a $30 loss and each reprocessed unit requires an extra 0.30 hours of processing time. The resource time of producing the original 200 units is 30 hours. As a result of a quality improvement program that was recently introduced, for each 200 units manufactured, the process now yields 190 conforming units, 1 unit to be scrapped, and the remaining units that must be reprocessed. Calculate the scrap cost for the new process.
2. Two products are manufactured in a machining center. The productions times per unit of products 1 and 2 are 10 and 12 minutes, respectively. The total regular machine time is 2500 minutes per day. In anyone day, the manufacturer can produce between 150 and 200 units of product 1, but no more than 45 units of product 2. Overtime may be used to meet the demand at an additional cost of $.50 per minute. Assuming that the unit profits for products 1 and 2 are $6.00 and $7.50, respectively, formulate the problem as an LP model, then solve it using TORA to determine the optimum production level for each product as well as any overtime needed in the center.
Motorking Corporation, a market leader in the production of specialized engine additives, is considering introducing a new "gas extender" product. This product is added to an automobile’s gasoline to extend mileage and reduce exhaust emissions. Motorking's manufacturing facility can produce 50,000 cases of the new product per year with a set-up cost of $100,000. The average variable cost per case would be $5. Large orders, (i.e., above 50,000 cases) will be subcontracted to a local refining company. Motorking has signed a secrecy agreement with the vendor that guards the basic process. The variable cost per case, if the new product is produced outside, is $9. Whether the product is manufactured by Motorking or by the vendor, there is a $12 per case cost for marketing and overhead. Motorking's production manager is considering three production levels for the new product: 50,000 cases, 75,000 cases, and 100,000 cases. The level of sales will depend on the state of the economy. Sales…
Assume that producing 1 unit of calcium requires 0.4 units of calcium, 0.2 units of hydrogen, and 0.5 units of sea salt; that producing 1 unit of hydrogen requires 0.2 units of calcium, 0.7 units of hydrogen, and 0 units of sea salt; and that producing 1 unit of sea salt requires 0.4 units of calcium, 0 units of hydrogen, and 0.5 units of sea salt. Find the production schedule that satisfies an external demand for 57 units of calcium, 33 units of hydrogen, and 8 units of sea salt. X =
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = at (x, y) = ( (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. scs (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. s (resource) s (d) Find the shadow price for the resource associated with the…
8. A factory manufactures two products, each requiring the use of three machines. The first machine can be used at most 70 hours, the second machine at most 40 hours, and the third machine at most 90 hours. The first product requires 2 hours on machine 1, 1 hour on machine 2. and 1 hour on machine 3; the second product requires 1 hour each on machines 1 and 2, and 3 hours on machine 3. If the profit is $40 per unit for the first product and $60 per unit for the second product, how many units of each product should be manufactured to maximize profit?

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